arXiv:2502.18659math.OCcs.NA2025-02中稿 · ed被引 1
多网格方法加速总变差图像反问题求解
Multigrid methods for total variation
- 交替使用粗细网格的前向后向分裂法
- 在去噪与磁共振成像中验证高效性
- 适合大规模图像重建任务
基于非光滑一致性条件，我们构建并证明了一种前向后向分裂方法的收敛性，该方法在精细网格与粗糙网格之间交替进行。研究聚焦于总变差正则化的逆成像问题，特别是其对偶问题，并详细设计了相应的粗网格问题。我们在总变差去噪和磁共振成像任务上展示了该方法的性能。
原文摘要 · Abstract (English)
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.
图像重建多网格总变差
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